 # Answer

(a) Pretty straightforward, just divide the whole length (240) by the shorter side of the tile (y-5)

(b) No. of tiles in top row = 240 / (y – 5)

Thus, no. of tiles in top and bottom row = 2 [ 240 / (y – 5) ]

No. of tiles in left column = 160 / y

Thus, no. of tiles in left and right column = 2 [ 160 / y ]

One must realise that by adding up both terms, the tiles in the corners are double-counted, so they actually add up to 44 + 4 = 48. From here, we can formulate an equation in terms of y.

2 [ 160 / y ] + 2 [ 240 / (y – 5) ] = 48

Simplifying, we have:

20 / y + 30 / (y – 5) = 3

20 (y – 5) + 30 y = 3 (y) (y – 5)

20 y – 100 + 30 y = 3 y^2 – 15 y

3 y^2 -65 y + 100 = 0//

(c) By using whichever method you’re comfortable with:

Method 1:

 3 y -5 – 5y y -20 – 60y 3 y ^ 2 + 100 – 65 y

Method 2:

Apply quadratic equation, a = 3, b = -65, c = 100

You’ll end up with y = 5/3 (rej since y > 5) or y = 20. Thus the shorter side will be 20 – 5 = 15.

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